Phase structure of NJL model with weak renormalization group

Understand

We analyze the chiral phase structure of the Nambu--Jona-Lasinio model at finite temperature and density by using the functional renormalization group (FRG).

• The renormalization group (RG) equation for the fermionic effective potential $V(\sigma;t)$ is given as a partial differential equation, where $\sigma:=\bar \psi\psi$ and $t$ is a dimensionless RG scale.
• When the dynamical chiral symmetry breaking (D$\chi$SB) occurs at a certain scale $t_c$, $V(\sigma;t)$ has singularities originated from the phase transitions, and then one cannot follow RG flows after $t_c$.
• In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the D$\chi$SB and to evaluate the dynamical mass and the chiral condensate in low energy scales.